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Computational Probability Applications

  • Book
  • © 2017

Overview

Editors:
  1. Andrew G. Glen

    1. Department of Mathematics and Computer Science, The Colorado College, Colorado Springs, USA

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    You can also search for this editor in PubMed   Google Scholar

  2. Lawrence M. Leemis

    1. Department of Mathematics, The College of William and Mary, Williamsburg, USA

    View editor publications

    You can also search for this editor in PubMed   Google Scholar

  • Explores the development and use of the modeling and computational capabilities in the Maple-based APPL programing language to solve real and important problems in probability
  • Highlights the uses of symbolic algebra with probabilistic/stochastic applications in variety of contexts
  • Authors are distinguished leaders in the field and development of computational methods for solving problems expressed using probability models
  • Includes supplementary material: sn.pub/extras

Part of the book series: International Series in Operations Research & Management Science (ISOR, volume 247)

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Table of contents (15 chapters)

  1. Front Matter

    Pages i-x
    Download chapter PDF

  2. Accurate Estimation with One Order Statistic

    • Andrew G. Glen
    Pages 1-13

  3. On the Inverse Gamma as a Survival Distribution

    • Andrew G. Glen
    Pages 15-30

  4. Order Statistics in Goodness-of-Fit Testing

    • Andrew G. Glen, Donald R. Barr, Lawrence M. Leemis
    Pages 31-39

  5. The “Straightforward” Nature of Arrival Rate Estimation?

    • Donald R. Barr, Andrew G. Glen, Harvey F. Graf
    Pages 41-50

  6. Survival Distributions Based on the Incomplete Gamma Function Ratio

    • Andrew G. Glen, Lawrence M. Leemis, Daniel J. Luckett
    Pages 51-58

  7. An Inference Methodology for Life Tests with Full Samples or Type II Right Censoring

    • Andrew G. Glen, Bobbie L. Foote
    Pages 59-73

  8. Maximum Likelihood Estimation Using Probability Density Functions of Order Statistics

    • Andrew G. Glen
    Pages 75-85

  9. Notes on Rank Statistics

    • Daniel J. Luckett, Samatha King, Lawrence M. Leemis
    Pages 87-106

  10. Control Chart Constants for Non-normal Sampling

    • William H. Kaczynski, Lawrence M. Leemis
    Pages 107-117

  11. Linear Approximations of Probability Density Functions

    • Lee S. McDaniel, Andrew G. Glen, Lawrence M. Leemis
    Pages 119-132

  12. Univariate Probability Distributions

    • Lawrence M. Leemis, Daniel J. Luckett, Austin G. Powell, Peter E. Vermeer
    Pages 133-147

  13. Moment-Ratio Diagrams for Univariate Distributions

    • Erik Vargo, Raghu Pasupathy, Lawrence M. Leemis
    Pages 149-164

  14. The Distribution of the Kolmogorov–Smirnov, Cramer–von Mises, and Anderson–Darling Test Statistics for Exponential Populations with Estimated Parameters

    • Diane L. Evans, John H. Drew, Lawrence M. Leemis
    Pages 165-190

  15. Parametric Model Discrimination for Heavily Censored Survival Data

    • A. Daniel Block, Lawrence M. Leemis
    Pages 191-215

  16. Lower Confidence Bounds for System Reliability from Binary Failure Data Using Bootstrapping

    • Lawrence M. Leemis
    Pages 217-237

  17. Back Matter

    Pages 239-256
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Keywords

About this book

This focuses on the developing field of building probability models with the power of symbolic algebra systems. The book combines the uses of symbolic algebra with probabilistic/stochastic application and highlights the applications in a variety of contexts. The research explored in each chapter is unified by the use of A Probability Programming Language (APPL) to achieve the modeling objectives. APPL, as a research tool, enables a probabilist or statistician the ability to explore new ideas, methods, and models. Furthermore, as an open-source language, it sets the foundation for future algorithms to augment the original code. 

Computational Probability Applications is comprised of fifteen chapters, each presenting a specific application of computational probability using the APPL modeling and computer language. The chapter topics include using inverse gamma as a survival distribution, linear approximations of probability density functions, and also moment-ratio diagrams for univariate distributions. These works highlight interesting examples, often done by undergraduate students and graduate students that can serve as templates for future work. In addition, this book should appeal to researchers and practitioners in a range of fields including probability, statistics, engineering, finance, neuroscience, and economics.

Reviews

“This volume successfully merges the use of symbolic algebra with stochastic applications and displays its applications in a host of situations. … The book organized sequentially, well structured, and chapters are self-contained. … The book is a good source as a reference book in a multitude fields. … this is a good contribution, providing up-to-date coverage on selected topics in a logical and systematic manner. Variability and diversity in research is the spice of the life!” (S. Ejaz Ahmed, Technometrics, Vol. 59 (3), July, 2017)

Editors and Affiliations

  • Department of Mathematics and Computer Science, The Colorado College, Colorado Springs, USA

    Andrew G. Glen

  • Department of Mathematics, The College of William and Mary, Williamsburg, USA

    Lawrence M. Leemis

About the editors

Dr. Andrew Glen is a Professor Emeritus of Operations Research from the United States Military Academy, in West Point, NY. He is currently a visiting professor at The Colorado College in Colorado Springs, Colorado. He is a retired colonel from the US Army, and spend 16 years on faculty at West Point. He has published three books and dozens of scholarly articles, mostly on the subject of computational probability. His research and teaching interests are in computational probability and statistical modeling. 

Lawrence Leemis is a professor in the Department of Mathematics at The College of William & Mary in Williamsburg, Virginia, U.S.A. He received his BS and MS degrees in mathematics and his PhD in operations research from Purdue University. He has also taught courses at Purdue University, The University of Oklahoma, and Baylor University. He has served as Associate Editor for the IEEE Transactions on Reliability, Book Review Editor for the Journal of Quality Technology, and an Associate Editor for Naval Research Logistics. He has published six books and over 100 research articles, proceedings papers, and book chapters. His research and teaching interests are in reliability, simulation, and computational probability.

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